Question

3x-2/4 - 2x+3/3=2/3-x​

Answer 1

Answer:

Given,43x−2−32x+3=32−x

\frac{3x-2}{4} - \frac{2x+3}{3} + x = \frac{2}{3}43x−2−32x+3+x=32

LCM of 3,4 = 12.

\frac{3(3x - 2) - 4(2x + 3) + 12x}{12} = \frac{2}{3}123(3x−2)−4(2x+3)+12x=32

\frac{9x - 6 - 8x - 12 + 12x}{12} = \frac{2}{3}129x−6−8x−12+12x=32

\frac{13x - 18}{12} = \frac{2}{3}1213x−18=32

13x - 18 = \frac{12 * 2}{3}13x−18=312∗2

13x - 18 = \frac{24}{3}13x−18=324

13x - 18 = 8

13x = 18 + 8

13x = 26

x = 26/13

x = 2.

Answer 2

$\huge{\underline{\underline{\mathfrak{Solution}}}}$

$\sf\implies\:\frac{3x - 2}{4} - \frac{2x + 3}{3} = \frac{2}{3 - x} \\ \\ \sf\implies \frac{3( 3x - 2) - 4(2x + 3) }{12} =\frac{2}{3 - x} \\ \\\sf\implies \frac{9x - 6 - 8x - 12}{12} = \frac{2}{3 - x} \\ \\ \sf\implies \frac{x - 18}{12} = \frac{2}{3 - x} \\ \\ \sf\implies (x - 18)(3 - x) = 12 × 2 \\ \\ \sf\implies \: x(3 - x) - 18(3 - x) = 24 \\ \\ \sf\implies\: 3x - {x}^{2} - 54 + 18x = 24 \\ \\\sf\implies\: {-x}^{2} + 21x = 24 + 54 \\ \\ \sf\implies\: {-x}^{2} + 21x = 78 \\ \\ \sf\implies\:{-x}^{2} + 21x - 78 = 0\\\\ \huge{\boxed{ {x}^{2} - 21x + 78=0}}$